Pythagoras of Samos is the Pre-Socratic philosopher and religious teacher whose movement combined mathematical inquiry, ascetic practice, and the doctrine of the transmigration of souls into one of the most influential single intellectual-religious frameworks of the ancient world.
pythagoras
The Pre-Socratic philosopher and religious teacher whose Pythagorean movement combined mathematical inquiry, ascetic practice, and the doctrine of the transmigration of souls, and whose influence on subsequent philosophy and mathematics has been continuous through the Western tradition.
Birth around 570 BCE on Samos, death around 495 BCE in Metapontum (southern Italy). Both dates approximate.
Introduction
Pythagoras of Samos is the Pre-Socratic philosopher and religious teacher whose movement combined mathematical inquiry, ascetic practice, and the doctrine of the transmigration of souls into one of the most influential single intellectual-religious frameworks of the ancient world. The Pythagorean movement Pythagoras founded around 530 BCE at Croton (in southern Italy) was at once a philosophical school, a religious community, and a political faction; its influence on Greek philosophy through Plato (whose Pythagorean elements shaped Western metaphysics) and on Western mathematics (the theorem that bears his name remains in the secondary-school curriculum 2,500 years later) has been continuous.
The biographical and doctrinal record on Pythagoras himself is uniquely difficult. Pythagoras wrote nothing, and the early Pythagorean community famously maintained secrecy about the doctrines and practices of the school. The later doxographical and biographical sources (especially Iamblichus, Porphyry, and Diogenes Laertius, all writing in the third and fourth centuries CE) mix authentic early Pythagorean material with the accretion of legend and later Neopythagorean construction. The scholarly task of separating the historical Pythagoras from the later Pythagorean tradition has been one of the most contested in ancient philosophy.
Life and biography
Pythagoras was born around 570 BCE on the island of Samos in the eastern Aegean. The biographical reports describe early travel: years of study with the Egyptian priests, with the Babylonian astronomers, with the Persian Magi (the reports vary). The reports may be later constructions designed to give Pythagoras's wisdom an exotic Eastern origin; what is historically credible is some period of Eastern travel during which Pythagoras encountered mathematical and religious traditions that shaped his subsequent thought.
Around 530 BCE Pythagoras moved from Samos to Croton, a Greek colony in southern Italy. There he founded the school-community that bears his name. The Pythagorean community at Croton controlled the political life of the city for several decades; the political dominance eventually provoked a violent reaction (around 510 BCE or somewhat later) in which the community's meeting house was burned and many leading Pythagoreans killed. Pythagoras himself escaped to nearby Metapontum, where he died around 495 BCE.
The Pythagorean movement survived the destruction at Croton and continued through the fifth and fourth centuries BCE in southern Italy and Sicily, with communities at Tarentum, Metapontum, and elsewhere. The Pythagorean Archytas of Tarentum (early fourth century BCE), a major mathematician and political leader, was Plato's friend and the figure through whom Plato's Pythagorean engagement was mediated.
The doctrines
The attribution of specific doctrines to the historical Pythagoras rather than to the later Pythagorean tradition is contested. The scholarly consensus identifies several doctrines as plausibly traceable to Pythagoras himself.
The transmigration of souls
The doctrine of metempsychosis — the transmigration of souls from one body to another after death — is attributed to Pythagoras by early sources (including Xenophanes, a near contemporary, in a fragment that mocks Pythagoras for claiming to recognize the voice of a dead friend in the cry of a beaten dog). The doctrine has religious-ethical implications: the soul is immortal and survives death; the soul's subsequent fate is determined by the moral character of the life just completed; the ethical-ascetic practices of the Pythagorean community (vegetarianism, abstention from certain foods, ritual purifications) were partly grounded in the recognition that other living beings might house transmigrated human souls.
The doctrine shaped subsequent Greek thought through Plato's appropriation in the Meno (the doctrine of anamnesis — learning as recollection of what the soul knew before birth), the Phaedo (the argument for the immortality of the soul), and the Republic (the Myth of Er at the end of Book X). The Platonic engagement with the doctrine is one of the major channels through which Pythagorean thought reached subsequent Western philosophy.
Number and the cosmos
The Pythagorean doctrine that all things are numbers (or that the principles of all things are numbers) is the doctrine most associated with the school. The inspiration was almost certainly the discovery of numerical relationships in music (the Pythagorean discovery that the musical intervals of the octave, the fifth, and the fourth correspond to the ratios 2:1, 3:2, and 4:3 between the lengths of vibrating strings). The recognition that the qualitative experience of musical harmony could be reduced to quantitative relationships suggested a generalization: the structures of the world generally might be reducible to numerical relationships.
The Pythagorean cosmology developed this insight substantially. The heavens were organized through numerical proportions; the movements of the heavenly bodies produced a music of the spheres (the harmonic relationships that mortals could not hear because they had been hearing them since birth and could not distinguish them from silence); the substances of the world could be analyzed through numerical structures. The framework anticipates the mathematical physics that would emerge from Galileo onward, and Galileo himself acknowledged the Pythagorean inheritance.
The tetractys and the perfect number
The Pythagorean reverence for the tetractys — the triangular figure of ten dots arranged in four rows (1+2+3+4=10) — was one of the most distinctive features of the community. The number ten was the perfect number; the tetractys was the figure that exhibited the generation of the perfect number from the first four integers; the Pythagorean oath was reportedly sworn by him who gave to our soul the tetractys.
The doctrine has been variously interpreted. The mathematical content (the properties of triangular numbers, the significance of the first four integers) is in its own right; the religious-ethical use of the mathematical structure as the object of veneration is the distinctive feature of the Pythagorean framework.
The Pythagorean theorem
The theorem that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides has been associated with Pythagoras for centuries, though the historical record is more complicated. The theorem was known to the Babylonians centuries before Pythagoras (substantial Babylonian tablets from the early second millennium BCE document cases of the theorem); the Pythagorean contribution may have been the first general proof of the theorem rather than the discovery of the relationship itself.
The theorem has been in the mathematical curriculum continuously for 2,500 years and is the single mathematical result most associated with a named ancient figure.
Reception
The ancient reception of Pythagoras and the Pythagorean tradition was substantial. Plato's engagement (especially through Archytas of Tarentum) made Pythagorean themes in subsequent Platonism. The Neopythagorean revival of the first century BCE through the first century CE (Nigidius Figulus, Apollonius of Tyana, Numenius of Apamea) extended the tradition into the late ancient and early Christian periods.
The Renaissance recovery through Marsilio Ficino and the Florentine Platonists treated Pythagoras as the source of a philosophia perennis (the perennial philosophy) that ran through the ancient mystery traditions. The modern engagement through Walter Burkert's Lore and Science in Ancient Pythagoreanism (1962, German; 1972, English) separated the historical evidence from the later accretions and shaped contemporary Pythagorean scholarship.
Continuing engagement
Major recent scholarly work includes Walter Burkert's foundational study, Carl Huffman's work on Philolaus and Archytas, Leonid Zhmud's Pythagoras and the Early Pythagoreans (2012), Charles Kahn's Pythagoras and the Pythagoreans (2001), and the new Loeb edition by Laks and Most (2016). Active scholarly debates concern the separation of historical Pythagoras from later Pythagorean tradition, the extent of Pythagoras's mathematical contributions, the relation between the mathematical and the religious-ascetic dimensions of the movement.
Further reading
- Pre-Socratic — the tradition Pythagoras helped shape
- Plato — the major successor whose work preserves Pythagorean themes
- Heraclitus — the contemporary whose critique of Pythagoras has been preserved
- Parmenides — the Eleatic philosopher whose city of Elea had Pythagorean associations
The Pre-Socratic philosopher and religious teacher whose movement combined mathematical inquiry, ascetic practice, and the doctrine of the transmigration of souls into one of the most influential single frameworks of the ancient world.